When does the subadditivity theorem for multiplier ideals hold?

Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.

     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Anomalies of ultrasonic velocity in high-Tc ceramics YBa2Cu3Oy and BiSrCaCu2Oy

Ultrasonic longitudinal velocity and adsorption have been measured in ceramic superconductors YBa₂Cu₃O_y with various porosity and also in BiSrCaCu₂O_y. A velocity drop of about 400 ppm was found at T_c only in the measurements on cooling. The magnitude of the velocity drop is anomalously large compared with the value expected from the thermodynamics. A hysteresis of velocity with respect to temperature was observed in all the samples studied. It is suggested that some structural change at pore size level is responsible for this phenomenon.     

Temperature dependence of the exafs spectrum in YBa2Cu3O7−δ compounds

The temperature dependence of the extended X-ray absorption fine structure (EXAFS) is studied in the high T_c superconductors, YBa₂Cu₃O_7−δ. The measurements were done at the Cu K-edge for samples of two orthorhombic phases (T_c≈90 K and ≈58 K, respectively) and a nonsuperconducting tetragonal phase. Interatomic distances and mean square relative displacements σ² for Cu-O bonds are determined by the least squares refinement. The results indicate that values of σ² increase near T_c for both the orthorhombic samples. It is concluded that this anomalous behavior related to T_c is caused by an anomalous vibration of oxygen atoms in the Ba-O layer. Changes in the Cu-O distances from 300 to 20 K are not found.     

Measurement of circular dichroism spectra of liquid/liquid interface by centrifugal liquid membrane method.

The direct measurement of the circular dichroism (CD) spectra of liquid/liquid interface has been achieved for the first time by the centrifugal liquid membrane (CLM) method combined with a conventional CD spectropolarimetry. In the sample chamber of the CD spectropolarimeter, a cylindrical glass cell containing small amounts of organic and aqueous phases was rotated at ca. 7000 rpm to generate a two-phase liquid membrane with a high specific interfacial area. The CD spectra of the J-aggregate of protonated 5,10,15,20-tetraphenylporphyrin formed at the toluene/sulfuric acid interface in the rotating cell have been measured. The results demonstrated the novelty and advantages of this method.     

Surface-enhanced Raman scattering from oleate-stabilized silver colloids at a liquid/liquid interface.

Oleate-stabilized silver colloids of 5-nm-diameter were adsorbed to a toluene/water interface, and surface enhanced Raman scattering (SERS) spectra from these colloids were measured under the total internal reflection (TIR) condition. From the observed spectra, we examined the states of oleate ions and toluene molecules on silver colloids at the liquid/liquid interfacial region. The TIR-SERS spectra of oleate ions showed stronger peaks of the carboxylate group and the ethylene group than those of alkyl chains. From these results, it was found that the oleate ions were adsorbed on the silver surface in two different ways at the liquid/liquid interface; the carboxylate group adsorbed in the organic phase side, while the ethylene group adsorbed in the aqueous phase side. The shifts of the toluene in the interfacial SERS spectra were identical to those of bulk toluene, though the relative intensities among the peaks were not same. This result suggested that the toluene was adsorbed with a weak interaction, but was significantly enhanced by the local electromagnetic field at the colloid surface.     

Simultaneous determination of serotonin and 5-hydroxyindole-3-acetic acid in human urine by automated precolumn derivatization and semi-microbore column liquid chromatography with fluorescence detection.

An improved high-performance liquid-chromatographic (HPLC) assay for the simultaneous determination of serotonin (5-HT) and 5-hydroxyindole-3-acetic acid (5-HIAA) in human urine is reported. Following the automated precolumn derivatization of urinary 5-HT and 5-HIAA with benzylamine, the derivatives are separated by isocratic elution on a reversed-phase C18 semi-microbore column, and are fluorometrically detected at an excitation wavelength of 345 nm and an emission wavelength of 480 nm. The detection limits of 5-HT and 5-HIAA are 7 and 5 nmol/l in urine (0.7 and 0.5 fmol/20-microl injection). The proposed automatic method permits a highly selective and sensitive determination of 5-HT and 5-HIAA in human urine without any sample purification.